My thoughts completely align with yours. It is often difficult to spot mistakes in your dissertation after having spent months writing it due to wrong framing or formatting inconsistencies. Your brain simply ceases to recognize them! Thus, this is where a professional editor really comes in handy.
For a dissertation hung up on, for an editor, one needs to search an editor who specializes in academic writing. A good editor will embrace clarity, the flow of arguments, grammar, and adherence to your formatting style (APA, MLA, Chicago, etc). Most editors will also show points where your arguments could be stronger or more concise, which is extremely helpful.
To find independent editors, I would recommend looking at LinkedIn or Reedsy. Many independent editors have doctorate Ph.D. degrees and academic backgrounds, and understand just what is expected from any dissertation in the universities. When on the lookout, always ask for some editing samples— this will put you so much more in the know about the styles of the editor, and help you see whether they are compatible with you.
For those on a tighter budget, some editors offer "light editing" options, in which they primarily focus on grammar, typos, and formatting, instead of heavy content editing. This is a good middle ground if you don't require extensive reworking.
Another trick: referrals or testimonials from other students. A reliable editor will have good feedback from pulling off writtens, especially of dissertations.
Editing is the final push to make the fruits of your hard work shine, so settle for nothing short of great. You will thank yourself for it once you submit a polished, professional dissertation that accurately reflects your effort.